Gravitation Question 6
Question 6 - 25 January - Shift 1
$T$ is the time period of simple pendulum on the earth’s surface. Its time period becomes x T when taken to a height $R$ (equal to earth’s radius) above the earth’s surface. Then, the value of $x$ will be:
(1) 4
(2) 2
(3) $\frac{1}{2}$
(4) $\frac{1}{4}$
Show Answer
Answer: (2)
Solution:
Formula: Effect of Altitude
At surface of earth time period
$T=2 \pi \sqrt{\frac{\ell}{g}}$
At height $h=R$
$g^{\prime}=\frac{g}{(1+\frac{h}{R})^{2}}=\frac{g}{4}$
$\therefore \quad xT=2 \pi \sqrt{\overline{(g / 4)}}$
$\Rightarrow xT=2 \times 2 \pi \sqrt{\frac{\ell}{g}}$
$\Rightarrow xT=2 T \Rightarrow x=2$
